Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Cauchy Problem: General Solutions

In course

MATH-106(f): Analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables. ...

Description

This lecture covers the general solutions of Cauchy problems, focusing on differential equations and integrating factors. The instructor explains the process step by step, providing examples and discussing the uniqueness and existence of solutions. Topics include homogeneous and inhomogeneous equations, as well as the structure of the solutions. The lecture concludes with a detailed explanation of finding general solutions and the associated methods.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (3)

David Valentin Strütt

Adélie Eliane Garin

Boris Buffoni

Official source

Related concepts (32)

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Delay differential equation

In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.

Related lectures (33)

General Solution of Homogeneous Second Order Linear Differential Equations

Covers the general solution of homogeneous second-order linear differential equations with constant coefficients and the concept of linear independence of solutions.

Method of Undetermined Coefficients

Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Ordinary Differential Equations: Second Order Linear Inhomogeneous

Covers the resolution of second-order linear ordinary differential equations with constant coefficients and a source term.

Differential Equations: General Solutions and Methods Log in to Mediaspace to watch this video

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Separable Differential Equations Log in to Mediaspace to watch this video